The pair have been drafted in as replacements for Tommy O'Donnell and Dan Leavy, who were injured ahead of last weekend's 38-3 trouncing of South Africa.
Murphy won the most recent of his 17 caps in the historic 40-29 victory over New Zealand in Chicago 12 months ago, while Reidy earned his second against Japan in June.
Two other squad members, prop John Ryan (calf) and wing Keith Earls (hamstring), will return to Munster this week for rehabilitation, while flank Peter O'Mahony has received stitches on his ear and will be monitored.
(Reporting By Nick Said; editing by John Stonestreet)
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